Answer:
2
Step-by-step explanation:
Start by simplifying the expression:
[tex]4(x-3)+5x-x^2[/tex]
Use distribution:
[tex]4x-4(3)+5x-x^2\\4x-12+5x-x^2[/tex]
Add like terms:
[tex]9x-12-x^2[/tex]
Now, substitute the given value of x into the expression:
[tex]9(2)-12-2^2\\18-12-4\\6-4\\2[/tex]
Answer:
2
Step-by-step explanation:
Given: 4(x − 3) + 5x − x²
x = 2Substitute 2 for the value of x in the expression and simplify:
➜ 4(2 − 3) + 5(2) − (2)²
➜ 4(−1) + 10 − 4
➜ -4 + 10 - 4
➜ 2
Therefore, the value of the expression when x equals 2 is 2.
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Evaluate.
10! over
6!(12-8)!
Answer: 210
Step-by-step explanation:
! means, for example, 6! = 6 * 5* 4 * 3 * 2 * 1
Given:
[tex]\displaystyle \frac{10!}{6!(12-8)!}[/tex]
Subtract:
[tex]\displaystyle \frac{10!}{6!(4)!}[/tex]
Distribute:
[tex]\displaystyle \frac{10!}{6!*4!}[/tex]
Expand:
[tex]\displaystyle \frac{10 * 9 * 8 * 7 * 6 * 5* 4 * 3 * 2 * 1}{(6 * 5* 4 * 3 * 2 * 1)*(4 * 3 * 2 * 1)}[/tex]
Cancel out (6*5*4*3*2*1) in both the top and bottom as they equal 1:
[tex]\displaystyle \frac{10 * 9 * 8 * 7 }{4 * 3 * 2 * 1}[/tex]
Multiply:
[tex]\displaystyle \frac{5,040 }{24}[/tex]
Divide:
210
One day in a sporting goods store, 34 people came in and made purchases while 14 people came in but didn't buy anything. What's an unsimplified ratio, as a fraction, of the number of people who made a purchase and the number of people who came into the store
Answer:
34/48
Step-by-step explanation:
So to answer this problem, we need to know two things:
1) The number of people who made a purchase
2) The number of people who came into the store
The problem gives us 1), which is 34.
The answer for 2) is 34+14, since that's the total number of people who came into the store. This means that the ratio is 34/48.
What is the area of the following triangle in square meters? Do not round your answer.
A
=
m
2
The area of the triangle will be 3240 square centimeters.
What is the triangle?A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.
The diagram is given below.
The height of the triangle is 120 cm and the base of the triangle is 54 cm.
Then the area of the triangle will be
Area = 1 / 2 x 120 x 54
Area = 3240 square cm
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Answer:
0.324
Step-by-step explanation:
PLS HELP! If Cyrus knows that △ABC∼△EDC and AB¯¯¯¯¯¯¯¯∥ED¯¯¯¯¯¯¯¯, how can he prove that line m passing through AB¯¯¯¯¯¯¯¯ has the same slope as line l passing through ED¯¯¯¯¯¯¯¯?
Answer:
AB and DE are parallel because they have the same slope.
Step-by-step explanation:
Slope of the line AB :
[tex]=\frac{\text{rise} }{\text{run} } =\frac{CA}{-BC} =\frac{12}{-8} =-\frac{3}{2}[/tex]
Slope of the line DE :
[tex]=\frac{\text{rise} }{\text{run} } =\frac{CE}{-DC} =\frac{9}{-6} =-\frac{3}{2}[/tex]
What is the area, in square units, of the polygon shown here?
A figure in the shape of a block letter L with a vertical height of 8 units and a length of 5 units is shown. The length of the top of the L is 2 units and the height of the right side of the L is 1 unit.
14 units2
16 units2
17 units2
19 units2
The area of a 2D form is the amount of space within its perimeter. The correct option is D.
What is an area?The area of a 2D form is the amount of space within its perimeter. It is measured in square units such as cm², m², and so on. To find the area of a square formula or another quadrilateral, multiply its length by its width.
The area of the L block will be the sum of the area of A and B. Therefore, the area can be written as,
Area of L block = Area of A + Area of B
= (7×2) units² + (1 × 5) units²
= 14units² + 5units²
= 19units²
Hence, the correct option is D.
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Stuck on this. 60 points!
Answer:
Statement 1 and 2
Step-by-step explanation:
If you take t^2 - 16t + 55 and find some of its graphical values, you will get:
Turning point: (8,-9)
Roots: (5,0) and (11,0)
When this graph is plotted and you imagine the x axis to be time (as stated in the question), each of the roots (x - intercept) must be when the swimmer goes under and when they come back up.
This means that the swimmer dived under the water at 5 seconds and came back up at 9, making the first 2 statements correct.
Now the fourth statement is ruled out.
The fifth statement is not plausible as the graph would have to have more than 2 roots for the swimmer to enter the water twice.
That leaves the third statement. If you imagine the depth of the swimmer to be the y axis of our imaginary graph, and we know that the y axis of the turning point is -9, that means that the swimmer's deepest dive was 9 feet under the water, ruling out the third statement too.
Hope this helps :D
Answer:
[tex]h(t)= (t-5)(t-11)[/tex]
The swimmer comes back up 11 seconds after the timer is started.
The swimmer dives into the water 5 seconds after the timer is started.
Step-by-step explanation:
Given function:
[tex]h(t)=t^2-16t+55[/tex]
To factor a quadratic in the form [tex]ax^2+bx+c[/tex],
find two numbers that multiply to [tex]ac[/tex] and sum to [tex]b[/tex]:
[tex]\implies ac=55[/tex]
[tex]\implies b=-16[/tex]
Two numbers that multiply to 55 and sum to -16 are: -11 and -5
Rewrite b as the sum of these two numbers:
[tex]\implies t^2-11t-5t+55[/tex]
Factorize the first two terms and the last two terms separately:
[tex]\implies t(t-11)-5(t-11)[/tex]
Factor out the common term (t - 11):
[tex]\implies (t-5)(t-11)[/tex]
Therefore, the given formula in factored form is:
[tex]h(t)= (t-5)(t-11)[/tex]
The swimmer's depth is modeled as h(t). Therefore, when h(t) = 0 the swimmer will be at the surface of the water.
[tex]\implies h(t)=0[/tex]
[tex]\implies (t-5)(t-11)=0[/tex]
[tex]\implies t-5=0\implies t=5[/tex]
[tex]\implies t-11=0 \implies t=11[/tex]
Therefore, the swimmer will be at the surface of the water at 5 s and 11 s.
The swimmer's maximum depth is the vertex of the function. The x-value of the vertex is the midpoint of the zeros. Therefore, the x-value of the vertex is t = 8.
Substitute t = 8 into the function to find the maximum depth:
[tex]\implies h(8)=8^2-16(8)+55=-9[/tex]
So the swimmer's maximum depth is 9 ft.
True Statements
The swimmer comes back up 11 seconds after the timer is started.
The swimmer dives into the water 5 seconds after the timer is started.
7. A triangle has an area of 20 in². If the height of the
triangle is 5 inches, find the base of the triangle.
Step-by-step explanation:
the area of a triangle is
baseline × height / 2
in our case
baseline × 5 / 2 = 20 in²
baseline × 5 = 40
baseline = 8 in
Jenny spins a fair 4-sided spinner what is the probabiliity that the spinner will land on a or b
Answer:
Step-by-step explanation:
jenny spin a fair-4 spinner
The probability that the spinner will land on a or b will be 0.50.
What is probability?Its fundamental concept is that someone will nearly surely occur. The proportion of positive events in comparison to the total of occurrences.
Then the probability is given as,
P = (Favorable event) / (Total event)
Jenny spins a fair 4-sided spinner.
Let the section be marked as a, b, c, and d.
Then the total number of the event will be given as,
Total events = 4
Then the probability that the spinner will land on a or b will be given as,
P = 1/4 + 1/4
P = (1 + 1)/4
P = 2/4
P = 1/2
P = 0.50
The probability that the spinner will land on a or b will be 0.50.
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2x(x-5) -x (3 + 2x) = 26
help me pls
Answer:
x = -2
Step-by-step explanation:
[tex]2x(x-5)-x(3+2x) = 26\\2x^{2} -10x-3x-2x^{2} = 26\\-13x=26\\x=\frac{26}{-13} \\=-2[/tex]
Its basically the order of operations, from left to right , evaluate brackets (if possible), then multiplication or division, lastly followed by addition or subtraction.
2x2-10x-3x-2x2=26
Eliminam opusele
reducem termenii
-13x=26
imparte ambele parti
x=-2
Step-by-step explanation:
Help!! Due tomorrow. x(x − 8) = 0
Answer: x = 0, 8
Step-by-step explanation:
x = 0
x - 8 = 0 ⇒ x = 8 (move 8 to the right)
x = 0, 8
Solve for x. Round to nearest tenth
SOMEONE PLEASE HELP ME WITH THIS ILL GIVE YOU BRAINLIST ANSWER
Image above
Answer:
x ≈ 0.5
Step-by-step explanation:
using the tangent ratio in the right triangle
tan63° = [tex]\frac{opposite}{adjacent}[/tex] = [tex]\frac{IJ}{JK}[/tex] = [tex]\frac{1}{x}[/tex] ( multiply both sides by x )
x × tan63° = 1 ( divide both sides by tan63° )
x = [tex]\frac{1}{tan63}[/tex] ≈ 0.5 ( to the nearest tenth )
Answer:
x = 0.5
Step-by-step explanation:
We can use tan Θ to find the value of x.
tan Θ = Opposite ÷ Adjacent
Let us solve it now
tan 63 = 1 ÷ x
1.9626 = 1 ÷ x
x = 1 ÷ 1.9626
x = 0.5095
x ≈ 0.5 ( nearest 10th )
1940 people attended a basketball game. 679 of the people attending supported the home team, while 1261 supported the visiting team. What percentage of people attending supported the home team?
Answer:
35%
Step-by-step explanation:
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
The percentage of people who supported the home team is 35%.
The percentage is calculated by dividing the required value by the total value and multiplying by 100.
Required percentage value = a
total value = b
Percentage = a/b x 100
Example:
50% = 50/100 = 1/2
20% = 20/100 = 1/5
25% = 25/100 = 1/4
We have,
Number of people who attended the basketball game = 1940
Number of people who supported the home team = 679
Number of people who supported the visiting team = 1261
The percentage of people who supported the home team.
= [ Number of people who supported the home team / Total number of people who attended the basketball game ] x 100
= [679 / 1940] x 100
= 67900 / 1940
= 35%
Thus,
The percentage of people who supported the home team is 35%.
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At what rate per cent per annum will rs 6000 amount to rs 6615 in two years when interest is compounded annually?
Answer: 5%
Step-by-step explanation:
[tex]6615=6000(1+r)^{2} \\ \\ 1.1025=(1+r)^{2} \\ \\ 1.05=1+r \\ \\ r=0.05=\boxed{5\%}[/tex]
please help!
[3 x 2⁵ - 13 x (-2)] + 2³
(-2² +3²) - 3
Give your answer in simplest form.
Answer:
122x + 37
Step-by-step explanation:
hope this helps u
Answer:
[3×2⁵+13×2]+2³(-2²+3²)-3=
[3×32+26]+2³(-4+9)-3=
[96+26]+2³(5)-3=
122+40-3
162-3=
159...
note:-a×(-b)=+ab
A factory made 424 items in 4 hours at a
constant rate. Plot the points on the graph
to represent the total number of items
made each hour.
ty
400
300
200
100
X
Items
0
1
2 3
Hours
4
A graph is a way to represent a lot of data in a visual format. The graph can be drawn as using the equation y=100x+24.
What is a graph?A graph is a way to represent a lot of data in such a visual format that it is easy for the user to understand the complete information in one go. Usually, the line of the graph is a function that follows the graph.
Given a factory-made 424 items in 4 hours at a constant rate. Also, the table is given, therefore, the slope of the line can be written as,
m = (400-300)/(4-3) = 100
Therefore, the equation can be written as y=100x+C
now, substituting the point we will get,
424 = 100(4) + C
424 - 400 = C
C = 24
Therefore, the graph can be drawn as using the equation y=100x+24.
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What is the area of a polygon with vertices of (-2,-4), (4,-4), (4, 4), and (-5, 4)?
216 square units
30 square units
120 square units
60 square units
Answer: 60 square units
Step-by-step explanation: i hope that helps buddy :)
Enter the number that belongs in the green box.
Answer:
the green box is 0
Step-by-step explanation:
we are asked to find the x-intercept, which means y = 0
(x, y)
Another way to test this is plug it in 1 for x! (1, y) where x = 1
[tex]y = \frac{2x^{2} -3x+1}{2x^{2} +8x+6} \\\\[/tex]
[tex]y = \frac{2(1)^{2} -3(1)+1}{2(1)^{2} +8(1)+6}[/tex]
[tex]y = \frac{2(1) -3(1)+1}{2(1) +8+6}[/tex]
[tex]y = \frac{2 - 3 + 1}{2 + 8 + 6}[/tex]
[tex]y = \frac{-1+1}{10 + 6}[/tex]
[tex]y = \frac{0}{16}[/tex]
y = 0
What is the center of the circle described by the equation (x-6)² + (y + 5)² = 25?
Reason:
Rewrite the given equation into [tex](x-6)^2 + (y-(-5))^2 = 5^2[/tex]
I changed the y+5 into y-(-5), and also replaced 25 with [tex]5^2[/tex]
Then compare that to the circle template of [tex](x-h)^2 + (y-k)^2 = r^2[/tex]
We see that h = 6 and k = -5 to give a center of (h,k) = (6, -5)
Side note: the radius is r = 5 units
Question 9 of 10
Which pairs of angles in the figure below are vertical angles?
Check all that apply.
Answer:
B and C
Step-by-step explanation:
vertical angles are angles that are opposite of each other when two lines cross. Vertical angles are congruent = they are equally large.
the angles listed in B and C are mirrored across either an imaginary or a directly visible line. and that makes them vertical angles.
Find CE.
Show your work!
The length of the chord CE is 24.46 in
To find the length of the chord CE, we solve the question using pythagoras' theorem
What is a chord?A chord is a line segment touching two points in a circle.
What is pythagoras' theorem?Pythagoras' theorem states that in any right angled triangle with sides a, b and c where c is the hypotenuse side, we have that
c² = a² + b²
The required triangle
Now form the diagram the radius of the circle BE forms a right angled triangle with the perpendicular to the chord, BO and the midway between the chord, OE.
BO = BD - OD
= 20 in - 5 in
= 15 in
From pythagoras,
BE² = DE² + BO²
making DE subject of the formula, we have
DE = √(BE² - BO²)
DE = √((20 in)² - (15 in)²)
DE = √(400 in² - 225 in²)
DE = √(175 in²)
DE = 13.23 cm
The length of the chord
Since the chord CE = 2DE,
So, CE = 2 × 13.23 in
= 26.46 in
So, the length of the chord CE is 24.46 in
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Calvin deposits $400 in a savings account that accrues 5% interest compounded monthly. after c years, calvin has $658.80. makayla deposits $300 in a different savings account that accrues 6% interest compounded quarterly. after m years, makayla has $613.04. what is the approximate difference in the number of years that calvin and makayla have their money invested?
The approximate difference in years for Calvin and Makayla is that B. Makayla invests her money 2 years longer.
Calculations and Parameters:Given:
Interest rate= 5%Deposit of Calvin= $400Final amount after c years= $658.80We use the compound interest formula,
[tex]A= P(1 + r/t)^t[/tex]
[tex]658.8/400= (1205/1200)^1^2^c[/tex]
c= 10 years approx.
For Makayla,
Amount deposited= $300Interest rate= 6%Final amount= $613.4m= ?We use the same formula:
[tex]A= P(1 + r/t)^t\\[/tex]
[tex]613.4/300= (1206/1200)^1^2^m[/tex]
m= 12 years approx.
Hence, the difference in the years would be:
12-10
= 2 years.
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Answer:
Makayla invests her money 2 years longer
Step-by-step explanation:
b on edge
3. Given the triangle below. Point T is the circumcenter. Point E bisects side MO. TE measures a length of 5. What is the length of MT? Round your answer to the nearest tenth.
Answer:
6.4
Step-by-step explanation:
E bisects side MO, plot it in the center of M and O
MO is 8, split into two even parts, 4 and 4
TE is 5
set up Pythagorean theorem, 5^2 + 4^2 = x^2 to find MT
25+16=x^2
41=x^2
x=6.403
Amelie wants to decorate the outside of the box but not the bottom. It is a 5 in. by 3 in. by 2 rectangular prism. If the beads that she is using cost $0.25 per square inch, how much will she pay for the beads? Her work is shown. surface area = 15 + 15 + 6 + 6 + 10 + 10 = 62 in. 2 cost = 0.25(62) = $15.50 Did she make an error? Yes, she should have only added the area of five of the six faces. Yes, she did not use the correct area formula for a rectangle. Yes, she calculated the cost incorrectly. No, she didn’t make any errors.
Answer:
Yes, she should have only added the area of five of the six faces.
Step-by-step explanation:
The formula for determining the surface area of a cuboid or box is expressed as
Surface area = 2lw + 2lh + 2wh
Where l, w and h represents length, width and height of the box respectively.
2lw represents the area of the top and the bottom of the box. Since she doesn't want to cover the bottom, it becomes lw. Therefore,
Surface area = 15 + 6 + 6 + 10 + 10 = 47 in².
The cost would be
0.25 × 47 = $11.75
Therefore,
Yes, she should have only added the area of five of the six faces.
If the perimeter of this triangle is 15 centimeters, what is the value of n?
The value of n from the triangle = 2.5
Calculation of perimeter of trianglePerimeter of a triangle= a +b+c
Where,
a= n
b= 5n - 6
C= 2n + 1
P= 15
Therefore n
15 = n + 2n + 1 + 5n - 6
15 = 8n-5
8n= 15+5
8n = 20
n= 20/8
n= 2.5
Therefore, the value of n = 2.5
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Please help! Giving brainlist!
f(x) =2x^2+4x-6. g(x)=4x^3-6x^2+3 find (f+g)(x)
Answer:
=4x³-4x²+4x-3
Step-by-step explanation:
(f+g)(x)=4x³+2x²-6x²+4x-6+3
=4x³-4x²+4x-3
13 = m/4 + 7 can you show work too
The correct value of this equation is m = 24
Resolution methodThis equation contains a fractional term. We note that the denominator of this equation is the term 4. Therefore, we will multiply the sides by 4:
13 = m/4 + 7
13 . 4 = 4(m/4) + 7 . 4
52 = m + 28
Now, let's isolate the variable "as negative" and after the equality - we'll be subtracting the terms:
52 = m + 28
-m = 28 - 58
-m = -24
m = 24
Therefore, the correct value of this equation will be m = 24
Question 4
1 pts
in 2013, the number of rabbits in a local park is 120, but this number is decreasing
each year by a constant percent. the number of rabbits in the park t years after 2013
can be found using the given formula. about how many rabbits will be left in the park
after 10 years?
r=120(0.99)
1,188
247
1
108
After 10 years, there will be 108 rabbits left in the park.
What is Exponential Equation?An exponential function is a function of form f (x) = aˣ, where “x” is a variable and “a” is a constant which is called the base of the function and it should be greater than 0.
Here, the given equation;
R = 120 (0.99)ⁿ
where, n is the number of years
n = 10 years (given)
R = 120 (0.99)¹⁰
R = 120 X 0.904
R = 108.52
Thus, After 10 years, there will be 108 rabbits left in the park.
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Which of the following is the solution set of 6x + 5 = -29?
O {-4}
O {-17/3)
O (17/3)
Answer:
-[tex]\frac{17}{3}[/tex]
Step-by-step explanation:
U.S. Birth Rate, 1950-2000
Year
Birth Rate
(per 1000 population)
1950
24.1
1960
23.7
1970
18.4
1980
15.9
1990
15.7
2000
14.7
Source: World Almanac 2003
Is the relation (year, birth rate) a function? Explain.
a.
No, there is a year with two birth rates paired with it.
b.
Yes, each year is paired with only one value for the birth rate.
c.
No, two years have a birth rate of over 20.
d.
No, there are no negative birth rate values.
Using it's concept, it is found that the correct option regarding whether the relation is a function is given by:
b. Yes, each year is paired with only one value for the birth rate.
When a relation represents a function?It represents a function if each value of the input is mapped to only one value of the output.
In this problem, the inputs are the decades(1950 to 2000), and each has only one rate, hence it is a function and option b is correct.
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